Viscopedia | A free encyclopedia for viscosity.

# Measuring Principles

The principles introduced in this section represent a cross-section from traditional to technically advanced methods.

## Introduction to the Gravimetric Capillary Principle

Measurements using capillary viscometers are based on the relation between viscosity and time. They use gravity as the driving force; therefore the results are kinematic viscosity values.

The big advantage of this method is that gravity is a highly reliable driving force. It is not artificially generated, so this avoids potential errors. Because gravity is available everywhere on earth and does not require further technical equipment, this principle is widely established in many standards and standardized practices.

The disadvantage of this principle is that the driving force cannot be varied. It is too small for highly viscous samples. Further, many different capillaries are required to cover a wide viscosity range with one constant driving force. For example, with Ubbelohde capillaries each can cover a range defined by its minimum viscosity times factor 5 (e.g. type 0B: 1 mm2/s to 5 mm2/s).

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## Capillary Types

Various different standardized glass capillaries are in use today. The capillaries are also referred to as 'tubes'.

There are direct-flow or reverse-flow capillaries available. In direct-flow capillaries the sample reservoir is located below the measuring marks; in reverse-flow types the reservoir sits above the marks. Reverse-flow capillaries allow the testing of opaque liquids and can have a third measuring mark. Having three measuring marks provides two subsequent flow times and can define the measurement's determinability.

Some frequently used types are the following:

1 ... Ostwald
2 ... Ubbelohde
3 ... Cannon-Fenske
4 ... Houillon

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## Physics of the Gravimetric Capillary Principle

A defined volume of liquid flows through a long capillary with an exactly defined inner diameter and length. The time the liquid takes to flow between two level marks is measured. A minimum flow time is defined for capillary viscometers to ensure that the flow conditions inside the capillary allow for laminar flow.

By calibrating each capillary with a fluid of known viscosity a factor is obtained. To get the sample's viscosity, its flow time is multiplied by the capillary factor.

## Introduction to the Rotational Principle

Though gravity is available everywhere for free, it is sometimes not strong enough as a driving force. For highly viscous fluids a measurement based on gravity would take far too long. Therefore, rotational viscometers use a motor drive. Unlike capillary viscometers, rotational viscometers provide dynamic or shear viscosity results.

A rotational viscometer consists of a sample-filled cup and a measuring bob that is immersed into the sample. There are two main principles in use:

In addition, there are different types of measuring devices based on the same principle and various shapes of measuring bobs to suit a great number of applications.

### The Couette Principle

If the bob stands still and the drive rotates the sample cup, this is the Couette principle (named after M. M. A. Couette, 1858 to 1943). Although this construction avoids problems with turbulent flow, it is rarely used in commercially available instruments. This is probably due to problems with the insulation and tightness of the rotating sample cup.

### The Searle Principle

In most industrially available viscometers the motor drives the measuring bob and the sample cup stands still. The viscosity is proportional to the motor torque that is required for turning the measuring bob against the fluid’s viscous forces. This is called the Searle principle (named after G. F. C. Searle, 1864 to 1954). When employing the Searle principle, the bob's rotational speed in low-viscosity samples should not be too high. Otherwise turbulent flow could occur due to centrifugal forces or the effects of inertia.

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## Physics of the Searle Principle

The motor turns a measuring bob or spindle in a container filled with sample fluid. While the driving speed is preset, the torque required for turning the measuring bob against the fluid’s viscous forces is measured.

1 …  Motor and measuring unit
2 …  User interface
3 …  Stand
4 …  Spindle/bob axis
5 …  Sample-filled cup
6 …  Measuring spindle/bob (rotor)

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## Rotational Device Types

In rotational viscometers there are two common approaches to measure the torque:

### Spring Devices

The motor - typically a stepper motor - drives the main shaft. A pivot and spring assembly rotates on the shaft. The spindle with the measuring bob (rotor) is attached to this assembly. As the spindle rotates, the spring is deflected proportional to the torque caused by the viscosity of the sample under test.

This system provides high measurement accuracy at the cost of covering only a small measuring range. The sensitive pivot bearing must be protected from undesirable influences and damage.

1 … Motor
2 … Upper slit disc
3 … Upper photo sensor
4 … Spring
5 … Pivot
6 … Lower photo sensor
7 … Lower slit disc
8 … Measuring bob (rotor)

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### Servo Devices

This viscometer type uses a servo motor to drive the main shaft. The spindle with the measuring bob (rotor) is attached directly to the shaft. A high-resolution digital encoder measures the rotational speed. The motor current is proportional to the torque caused by the viscosity of the sample under test. The viscosity can be computed based on rotational speed and current.

Compared to models with a pivot bearing and spring systems, viscometers with a servo motor cover a wider measuring range and are more robust. The electronic decoder and motor allow for greater torque and speed ranges than is possible with a mechanical spring. However, the accuracy for low speeds and low viscosity is lower than for spring systems, as the friction of the motor and bearing influences the measurement.

1 … Servo motor with high-resolution current measurement
2 … High-resolution optical encoder
3 … Encoder disc
4 … Measuring bob (rotor)

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## Rotational Measuring Systems

By changing the measuring system the rotational viscometer can be adapted to various applications. The most common spindles are listed below.

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### Spindles with special shapes

1 … T-bar spindle
2 … Krebs spindle
3 … Paste spindle
4… Vane spindle

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### Coaxial cylinders

This geometry is found in special adapters for small sample volume and in thermo-controlled cells. In contrast to measuring systems of undefined geometry, the shear rate and shear stress can be computed.

The shear rate at the surface of the bob can be calculated from the system's geometry and the angular velocity. Likewise, the shear rate can be calculated from the measured torque and the geometry. With shear rate and shear stress, you get the dynamic viscosity.

## Introduction to the Principle of the Stabinger Viscometer™

The Stabinger ViscometerTM was first established in the year 2000. It was then an entirely new design, combining the accuracy of kinematic viscosity determination with a wide measuring range. The Stabinger ViscometerTM  is a modification of the classic Couette-type rotational viscometer. It consists of two concentric cylinders where the outer one provides the driving force.

## Physics of the Stabinger Viscometer™

1 ... Outer tube (preset constant speed)
2 ... Sample liquid
3 ... Freely floating rotor (measured speed)
4 ... Magnet
5 ... Soft iron ring
6 ... Copper housing
7 ... Hall-effect sensor

The outer cylinder of the Stabinger Viscometer™ is a tube that rotates at constant speed in a temperature-controlled copper housing. The hollow internal cylinder – shaped as a conical rotor – is lighter than the filled samples and therefore floats freely within them, centered by centrifugal forces. In this way all bearing friction, an inevitable factor in most rotational devices, is fully avoided. The rotating fluid's shear forces drive the rotor, while a magnet inside the rotor forms an eddy current brake with the surrounding copper housing. An equilibrium rotor speed is established between the driving and retarding forces. This is an unambiguous measure of the dynamic viscosity.

The viscosity is inversely proportional to the speed difference between the outer tube and the inner rotor. This means the lower the sample's viscosity is, the greater the speed difference will be. This is because a less viscous sample transmits less of the outer tube's speed to the floating rotor.

The equilibrium speed is reached when the driving torque MD of the rotor and the retarding torque MR of the rotor are equal.

MD ... driving torque of inner rotor

MR ... retarding torque of inner rotor

n1 ... speed of inner rotor

n2 ... speed of outer tube

K1, K2, K ... constants; K is determined during adjustment.

The speed and torque measurement is implemented without direct contact by a Hall-effect sensor counting the frequency of the rotating magnetic field. This allows for a highly precise torque resolution of 50 pNm and a wide measuring range from 0.2 to 20,000 mPa.s with a single measuring system. A built-in density measurement based on the oscillating U-tube principle allows the determination of kinematic viscosity from the measured dynamic viscosity.

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## Introduction to the Rolling- / Falling-Ball Principle

The rolling-ball principle uses gravity as the driving force. A ball rolls through a closed capillary filled with sample fluid which is inclined at a defined angle. The time it takes the ball to travel a defined measuring distance is a measure for the fluid’s viscosity. The inclination angle of the capillary permits the user to vary the driving force. If the angle is too steep, the rolling speed causes turbulent flow. For calculating the viscosity from the measured time, the fluid’s density and the ball density need to be known.

Instruments that perform at inclination angles between 10° and 80° are rolling-ball viscometers. If the inclination angle is 80° or greater, the instrument is referred to as a falling-ball viscometer. Apart from balls as falling objects there are other viscometers which use rods or needles. Another variety of this principle is the bubble viscometer, which registers the rising time of an air bubble in the sample over a defined distance. The oscillating piston viscometer (ASTM D 7483) is an exception: It does not rely on gravity as the driving force but uses electromagnetic force to pull a magnetic cylinder through the sample.

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## Physics of the Rolling- / Falling-Ball Principle

FG … Effective component of gravity
FB … Effective component of buoyancy
FV … Viscous force

The following forces have a dominating influence on the rolling ball: While gravity pulls the ball downwards, the buoyancy inside the liquid and the liquid's viscosity oppose the gravitational force. The stronger the viscous force is, the slower the ball rolls.

To calculate the sample’s viscosity from the rolling time, the gravitational and buoyancy influence have to be considered. While the influence of gravity (FG) depends on the ball's density and volume, an object's buoyancy depends also on the liquid's density. This is why both the density of the liquid and the density of the ball need to be known to obtain a viscosity result.